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when the Italian mathematician Vito Volterra pointed out a
serious mistake in her work on the refraction of light in crystal-
line media. This oversight had escaped Weierstrass, who at the
time was so overwhelmed with official duties that outside of
them he had 'time only for eating, drinking, and sleeping. ...
In short', he says, 'I am what the doctors call brain-weary.' He
was now nearly seventy. But as his bodily ills increased his
intellect remained as powerful as ever.
The master's seventieth birthday was made the occasion for
public honours and a gathering of his disciples and former pupils
from all over Europe. Thereafter he lectured publicly less and
less often, and for ten years received a few of his students at his
own house. When they saw that he was tired out they avoided
mathematics and talked of other things, or listened eagerly
while the companionable old man reminisced of his student
pranks and the dreary years of his isolation from all scientific
friends. His eightieth birthday was celebrated by an even more
impressive jubilee than his seventieth and he became in some
degree a national hero of the German people.
One of the greatest joys Weierstrass experienced in his de-
clining years was the recognition won at last by his favourite
pupil. On Christmas Eve, 1888, Sonja received in person the
Bordin Prize of the French Academy of Sciences for her memoir
On the rotation of a solid body about a fixed point*
As is the rule in competition for such prizes, the memoir had
been submitted anonymously (the author's name being hi a
sealed envelope bearing on the outside the same motto as that
inscribed on the memoir, the envelope to be opened only if the
competing work won the prize), so there was no opportunity for
jealous rivals to hint at undue influence. In the opinion of the
judges the memoir was of such exceptional merit that they
raised the value of the prize from the previously announced
3,000 francs to 5,000. The monetary value, however, was the
least part of the prize.
Weierstrass was overjoyed. *I do not need to tell you*, he
writes, 'how much your success has gladdened the hearts of
myself and my sisters, also of your friends here. I particularly
experienced a true satisfaction; competent judges have now
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